Is there a way in LrC to make a thin white border inside the image boundary.

I, agree with Jim Wilde’s post. The plugin is very flexible with great features. I have used it from Lightroom 3.

You can hack the print module for this. Either use Print module -> stroke border (can only go to a maximum of 20 points so you would need to do some math), or set the page size to the correct output size you want and set the margins to 1 cm and the page background color to white and export to jpg from that.

If you are working to a standard image aspect ratio and orientation, an overlay frame graphic (made specifically for that aspect ratio, transparent apart from some lines or whatever, saved in PNG) can be applied in one of two ways. Either as a loupe overlay image (which is then seen in Develop etc, and would get included in an export)... or else, as an overlay in a page setup, Print module. Then "print" the image, or images, to JPG files. 

If you do not mind rounded corners, then there is a way in Lightroom itself. Go to the Effects panel and set Vignette all the way to +100, Roundness to -100, Feather to 0 and then move the Midpoint to get the width you want.

You should be able to achieve that using the Lr/Mogrify2 plug-in: https://www.photographers-toolbox.com/products/lrmogrify2.php

Note, this is an export plug-in, i.e. the border would only be applied on the exported file.